Theoretical Calculations of Infrared Bands of CH₃⁺ and CH₅⁺

Existing theoretical calculations predict that infrared spectra of the two most fundamental reactive carbo-ions, methyl cation $CH{_3}^+$ with $D_{3h}$ symmetry and protonated methyl cation $CH{_5}^+$ with $C_s(I)$, $C_s(II)$, and $C_{2v}$ symmetries, appear together in the 7-${\mu}m$ region corresponding to the C-H bending modes. Vibrational band profiles of $CH{_3}^+$ and $CH{_5}^+$ have been compared by ab initio calculation methods that use the basis sets of MP2/aug-cc-pVTZ and CCSD(T)/cc-pVTZ. Our results indicate that the bands of rotation-vibration transitions of $CH{_3}^+$ and $CH{_5}^+$ should overlap not only in the 3-${\mu}m$ region corresponding to the C-H stretching modes but also in the 7-${\mu}m$ region corresponding to the C-H bending modes. Five band intensities of $CH{_5}^+$ among fifteen vibrational transitions between 6 and 8 ${\mu}m$ region are stronger than those of the ${\nu}_2$ and ${\nu}_4$ bands in $CH{_3}^+$. Ultimate near degeneracy of the two bending vibrations ${\nu}_2$ and ${\nu}_4$ of $CH{_3}^+$along with the stronger intensities of $CH{_5}^+$ in the three hydrogen scrambling structures may cause extreme complications in the analysis of the high-resolution carbo-ion spectra in the 7-${\mu}m$ region.